Absolute maxima and minima a. Find the critical points of f on the given interval. b. Determine the absolute extreme values off on the given interval. c. Use a graphing utility to confirm your conclusions. f? (x) = cos (x) on [0,?]

Step-by-Step Solution:

Step 1 of 3

STEP_BY_STEP SOLUTION Step-1 Let f be a continuous function defined on an open interval containing a number ‘c’.The number ‘c’ is critical value ( or critical number ). If f (c) = 01 1 or f (c) is undefined. A critical point on that graph of f has the form (c,f(c)). Step-2 When an output value of a function is a maximum or a minimum over the entire domain of the function, the value is called the absolute maximum or the absolute minimum. Let f be a function with domain D and let c be a fixed constant in D. Then the output value f(c) is the 1. Absolute maximum value of f on D if and only if f(x) f(c) , for all x in D. 2. Absolute minimum value of f on D if and only if f(c) f(x) , for all x in D. Step_3 a). The given function is f(x) = cos (x) , on [0 , ].Clearly the function is a trigonometric function and it is continuous for all of x , and also the function is even function it gives only positive values. Now , we have to find out the critical points of f on the given interval. 2 Now , f(x) = cos (x) then differentiate the function both sides with respect to x. 1 d 2 f (x) = dx(cos (x)) d = 2cos(x) dx(cos(x)) , [ since dx( x ) = nx n1 and dx (cos (x )) = -sin( x )n dx ( x )] = -2cos(x) sin(x) = -sin(2x) , since by the formula Since ,...

Password Reset Request Sent
An email has been sent to the email address associated to your account.
Follow the link in the email to reset your password.
If you're having trouble finding our email please check your spam folder